Massive tuesday taken as holiday edit.
This commit is contained in:
Robin Clark
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@ -1006,6 +1006,12 @@ ISSN={1530-2059},}
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YEAR = "1988"
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}
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@BOOK{rdh,
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AUTHOR = "F~Langford-Smith",
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TITLE = "Radio designers Handbook: Fourth Edition",
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PUBLISHER = "ILIFFE",
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YEAR = "1953"
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}
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@BOOK{wdycwopt,
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AUTHOR = " Richard~P~Feynman",
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@ -44,7 +44,7 @@ are based on statistical thresholds for the frequency of dangerous failures.
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We could state, for instance, that we can tolerate an `acceptable' maximum number of
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dangerous failures per billion hours of operation.
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%
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We can then broadly categorise ratings of failure rates into Safety Integrity Levels (SIL)~\cite{scsh}.
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We can then broadly categorise orders of failure rates into Safety Integrity Levels (SIL)~\cite{scsh}.
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%
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So for a maximum of 10 potentially dangerous failures per billion hours of operation we assign a SIL level of 4,
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for 100 a SIL level of 3, and so on in powers of ten.
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@ -61,8 +61,8 @@ such as a nuclear power-station or air-liner,
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with far greater consequences on dangerous failure
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may require a SIL rating of 4.
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%
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What we are saying is that while we may tolerate a low incidence of failure on a band-saw,
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we will only tolerate extremely low incidences of failure in nuclear plant.
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That is while a low incidence of failure may be tolerable on a band-saw,
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extremely low incidences of failure would be tolerable in a nuclear plant.
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SIL ratings provide another objective yardstick for the measurement of system safety.
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%governing failure conditions and determining risk levels associated with systems.
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@ -90,7 +90,7 @@ and using contract programmed software, allows the modelling of integrated
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software/electrical systems.
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%
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This is followed by two chapters showing examples of the new modular FMEA analysis technique (Failure Mode Modular De-Composition FMMD)
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firstly looking at common electronic circuits and then at electronic/software hybrid systems.
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firstly looking at a variety of common electronic circuits and then at electronic/software hybrid systems.
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}
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\section{Motivation}
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@ -134,8 +134,8 @@ Any of the components that could, in failing, create a dangerous state were alre
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documented and approved using failure mode effects analysis (FMEA).
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%
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This new requirement
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effectively meant that all single and double component failures were
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now required to be analysed.
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effectively meant that single and double component failures were
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now required to be analysed~\cite{en298}[9.1.5].
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%
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This, from a state explosion problem alone,
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meant that it was going to be virtually impossible to perform.
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@ -1,25 +1,6 @@
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%\clearpage %\pagenumbering{arabic}
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%
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% %% NEED TWO MORE EXAMPLES --- 02JUN2012
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%
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% * ENVIRONMENTAL CASE (perhaps temp on an opto-coupler
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%
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% * OPERATIONAL STATE (perhaps a self test on an ADC where it is set to output and driven high and low and read)
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% to do: 23SEP2012
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%
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% 90_degrees is an incorrect failure mode in bubba and must be purged
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%
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% summing junction in sigma delta is not a valid fg, prob have to include
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% the op-amp....
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%
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% very annoying to have to pull out the comparison complexity.
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% makes the comparisons between approaches have less meaning.
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% have to discuss this.
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\label{sec:chap5}
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%
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This chapter demonstrates FMMD applied to
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a variety of typical electronic circuits including analogue and digital
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%and electronics/software
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@ -68,21 +49,19 @@ by applying FMMD to a sigma delta ADC.
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%analogue and digital signals.
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\item Section~\ref{sec:Pt100} demonstrates FMMD being applied to a commonly used Pt100
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safety critical temperature sensor circuit, this is analysed for single and then double failure modes.
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\end{itemize}
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%
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%~\ref{sec:chap4}
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%can be re-used. %, but with provisos.
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%
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%The first
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%(see section~\ref{sec:diffamp})
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%
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%
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%
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%
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%
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%
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%
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% Moving Pt100 to metrics
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%
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@ -91,7 +70,7 @@ safety critical temperature sensor circuit, this is analysed for single and then
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%and the analysis of double simultaneous failure modes.
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%
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% Now in CHAPTER 6: Finally section~\ref{sec:elecsw} demonstrates FMMD analysis of a combined electronic and software system.
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%
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% \section{Basic Concepts Of FMMD}
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%
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% The %idea
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@ -149,16 +128,14 @@ safety critical temperature sensor circuit, this is analysed for single and then
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% % \item {\dc} - a new component derived from an analysed {\fg}
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% % \end{itemize}
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%
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%
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%%%% XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
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%
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% This section might fit in with the literature review.... Chris thinks its not relevant here
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% and I agree 20OCT2012
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%
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%%%% XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
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%
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% % \section{ FMMD overview}
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% %
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% % In the next sections we apply FMMD to electronic circuits, analogue/digital and electronic/software hybrids.
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@ -244,12 +221,12 @@ safety critical temperature sensor circuit, this is analysed for single and then
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% %
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% %
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% %
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%
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\clearpage
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\section{Example Analysis: Inverting OPAMP}
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%
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\label{sec:invamp}
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%
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\begin{figure}[h]
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\centering
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\includegraphics[width=200pt]{CH5_Examples/invamp.png}
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@ -257,16 +234,16 @@ safety critical temperature sensor circuit, this is analysed for single and then
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\caption{Inverting Amplifier Configuration}
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\label{fig:invamp}
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\end{figure}
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%
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%This configuration is interesting from methodology pers.
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There are two obvious ways in which we can model this circuit.
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One is to do this in two stages, by considering the gain resistors to be a potential divider
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and then combining it with the OPAMP failure mode model.
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The second is to place all three components in one {\fg}.
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Both approaches are followed in the next two sub-sections.
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%
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\subsection{First Approach: Inverting OPAMP using a Potential Divider {\dc}}
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%
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Ideally we would like to re-use {\dcs} from the $PD$ from section~\ref{subsec:potdiv}, which on initial inspection, %at first glance,
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looks a good candidate for this.
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%
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@ -290,7 +267,7 @@ and analyse it as such; see table~\ref{tbl:pdneg}.
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We assume a valid range for the output value of this circuit.
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Thus negative or low voltages can be considered as LOW
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and voltages higher than this range considered as HIGH.
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%
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\begin{table}[h+]
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\caption{Inverted Potential divider: Single failure analysis}
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\begin{tabular}{|| l | l | c | c | l ||} \hline
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@ -304,7 +281,7 @@ and voltages higher than this range considered as HIGH.
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\end{tabular}
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\label{tbl:pdneg}
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\end{table}
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%
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\begin{figure}[h]
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\centering
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\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
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@ -342,18 +319,18 @@ and voltages higher than this range considered as HIGH.
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\path (R1SHORT) edge (PDHIGH);
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\end{tikzpicture}
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%
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\caption{Failure symptoms of the `Inverted Potential Divider' $INVPD$}
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\label{fig:pdneg}
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\end{figure}
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%
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%
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We can form a {\dc} from the analysis results in table~\ref{tbl:pdneg} %this,
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and call it an inverted potential divider $INVPD$.
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%
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We can now progress to the final stage of analysis for this amplifier,
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by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$.
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%
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\begin{table}[h+]
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\caption{Inverting Amplifier: Single failure analysis using the $PD$ {\dc}}
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\begin{tabular}{|| l | l | c | c | l ||} \hline
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@ -376,11 +353,11 @@ by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$.
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\end{tabular}
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\label{tbl:invamppd}
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\end{table}
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%
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%
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%%This gives the same results as the analysis from figure~\ref{fig:invampanalysis}.
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%
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%
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\begin{figure}[h+]
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\centering
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\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
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@ -475,8 +452,8 @@ by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$.
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\caption{Full DAG representing failure modes and symptoms of the Inverting Op-amp Circuit}
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\label{fig:invdag1}
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\end{figure}
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%
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%
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%The differences are the root causes or component failure modes that
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%lead to the symptoms (i.e. the symptoms are the same but causation tree will be different).
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We can now express the failure modes for the {\dc} $INVAMP$ thus;
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@ -486,9 +463,9 @@ We can draw a DAG representing the failure mode behaviour of
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this amplifier (see figure~\ref{fig:invdag1}). Note that this allows us
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to traverse from system level, or top failure modes to base component failure modes.
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%%%%% 12DEC 2012 UP to here in notes from AF email.
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%
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\clearpage
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%
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\subsection{Second Approach: Inverting OpAmp analysing with three components in one larger {\fg}}
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\label{subsec:invamp2}
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Here we analyse the same problem without using an intermediate $PD$
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@ -504,10 +481,10 @@ This concern is re-visited in the differencing amplifier example in the next sec
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%to symptoms) we cannot have a component failure mode that maps to two different symptoms (within a functional group).
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%Note that here we have a more general symptom $ OUT OF RANGE $ which could mean either
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%$HIGH$ or $LOW$ output.
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%
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% 08feb2012 bugger considering -ve input. It complicates things.
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% maybe do an ac amplifier later at some stage.
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%
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\begin{table}[h+]
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\caption{Inverting Amplifier: Single failure analysis: 3 components}
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\begin{tabular}{|| l | l | c | c | l ||} \hline
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@ -1919,6 +1896,7 @@ and is a well known safety critical circuit.
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Applying FMMD lets us look at this circuit in a fresh light.
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We analyse this for both single and double failures,
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in addition it demonstrates FMMD coping with component parameter tolerances.
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%
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The circuit is described traditionally and then analysed using the FMMD methodology.
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@ -1966,11 +1944,14 @@ industrial applications below 600\oc, due to high accuracy\cite{aoe}.
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\label{Pt100range}
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The Pt100 four wire circuit uses two wires to supply a small electrical current,
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and returns two sense voltages by the other two.
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%
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By measuring voltages
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from sections of this circuit forming potential dividers, we can determine the
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resistance of the platinum wire sensor. The resistance
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resistance of the platinum wire sensor.
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%
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The resistance
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of this is directly related to temperature, and may be determined by
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look-up tables or a suitable polynomial expression.
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look-up tables~\cite{eurothermtables} or a suitable polynomial expression.
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%
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%
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\begin{figure}[h]
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@ -2055,8 +2036,8 @@ Where this occurs a circuit re-design is probably the only sensible course of ac
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\fmodegloss
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\paragraph{Single Fault FMEA Analysis of $Pt100$ Four wire circuit.}
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\label{fmea}
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\label{sec:singlePt100FMEA}
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%\label{fmea}
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The Pt100 circuit consists of three resistors, two `current~supply'
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wires and two `sensor' wires.
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Resistors, are considered to fail by either going OPEN or SHORT (see section~\ref{sec:res_fms}). %circuit\footnote{EN298:2003~\cite{en298} also requires that components are downrated,
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@ -2144,25 +2125,25 @@ tables \cite{eurothermtables}, this corresponded to the resistances \ohms{100}
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and \ohms{212.02} respectively. From this the potential divider circuit can be
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analysed and the maximum and minimum acceptable voltages determined.
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These can be used as bounds results to apply the findings from the
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Pt100 FMEA analysis in section \ref{fmea}.
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Pt100 FMEA analysis in section\ref{sec:Pt100floating}. %\ref{fmea}.
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%
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As the Pt100 forms a potential divider with the \ohms{2k2} load resistors,
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the upper and lower readings can be calculated thus:
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%
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%
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$$ highreading = 5V.\frac{2k2+Pt100}{2k2+2k2+pt100} $$
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$$ lowreading = 5V.\frac{2k2}{2k2+2k2+Pt100} $$
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So by defining an acceptable measurement/temperature range,
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and ensuring the
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values are always within these bounds, we can be confident that none of the
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resistors in this circuit has failed.
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%
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To convert these to twelve bit ADC (\adctw) counts:
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%
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$$ highreading = 2^{12}.\frac{2k2+Pt100}{2k2+2k2+pt100} $$
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$$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+Pt100} $$
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%
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%
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\begin{table}[ht]
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\caption{Pt100 Maximum and Minimum Values} % title of Table
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\centering % used for centering table
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@ -2181,12 +2162,12 @@ $$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+Pt100} $$
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\end{tabular}
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\label{ptbounds}
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\end{table}
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%
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Table \ref{ptbounds} gives ranges that determine correct operation. In fact it can be shown that
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for any single error (short or opening of any resistor) this bounds check
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will detect it.
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%
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%
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% WAS a repeated paragraph
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% \paragraph{Consideration of Resistor Tolerance.}
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% %
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@ -2219,14 +2200,14 @@ will detect it.
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% will be determined by the accuracy of $R_2$ and $R_{3}$. It is reasonable to
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% take the mean square error of these accuracy figures~\cite{probstat}.
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%
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%
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\paragraph{Single Fault FMEA Analysis of $Pt100$ Four wire circuit}
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%
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%
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\ifthenelse{\boolean{pld}}
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{
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\paragraph{Single Fault Modes as PLD}
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%
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The component~failure~modes in table \ref{ptfmea} can be represented as contours
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on a PLD diagram.
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Each test case, is defined by the contours that enclose
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@ -2241,23 +2222,23 @@ and are thus enclosed by one contour each.
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\label{fig:Pt100_tc}
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\end{figure}
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} % \ifthenelse {\boolean{pld}}
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%
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%ating input Fault
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This circuit supplies two results, the {\em sense+} and {\em sense-} voltage readings.
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To establish the valid voltage ranges for these, and knowing our
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valid temperature range for this example ({0\oc} .. {300\oc}) we can calculate
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valid voltage reading ranges by using the standard voltage divider equation \ref{eqn:vd}
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for the circuit shown in figure \ref{fig:vd}.
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%
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%
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%
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%
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\paragraph{Proof of Out of Range Values for Failures}
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\label{pt110range}
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Using the temperature ranges defined above we can compare the voltages
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we would get from the resistor failures to prove that they are
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`out of range'. There are six test cases and each will be examined in turn.
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`out~of~range'. There are six test cases and each will be examined in turn.
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%
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\subparagraph{ TC 1 : Voltages $R_1$ SHORT }
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With Pt100 at 0\oc
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$$ highreading = 5V $$
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@ -2267,19 +2248,19 @@ $$ lowreading = 5V.\frac{2k2}{2k2+100\Omega} = 4.78V$$
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With Pt100 at the high end of the temperature range 300\oc.
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$$ highreading = 5V $$
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$$ lowreading = 5V.\frac{2k2}{2k2+212.02\Omega} = 4.56V$$
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%
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Thus with $R_1$ shorted both readings are outside the
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proscribed range in table \ref{ptbounds}.
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%
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\paragraph{ TC 2 : Voltages $R_1$ OPEN }
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%
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In this case the 5V rail is disconnected. All voltages read are 0V, and
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therefore both readings are outside the
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proscribed range in table \ref{ptbounds}.
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%
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%
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\paragraph{ TC 3 : Voltages $R_2$ SHORT }
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%
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With Pt100 at 0\oc
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$$ lowreading = 0V $$
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Since the lowreading or sense- is directly connected to the 0V rail,
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@ -2290,35 +2271,35 @@ $$ highreading = 5V.\frac{212.02\Omega}{2k2+212.02\Omega} = 0.44V$$
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%
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Thus with $R_2$ shorted both readings are outside the
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proscribed range in table \ref{ptbounds}.
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%
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\paragraph{ TC 4 : Voltages $R_2$ OPEN }
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Here there is no potential divider operating and both sense lines
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will read 5V, outside of the proscribed range.
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%
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%
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\paragraph{ TC 5 : Voltages $R_3$ SHORT }
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%
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Here the potential divider is simply between
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the two 2k2 load resistors. Thus it will read a nominal;
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2.5V.
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%
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Assuming the load resistors are
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precision components, and then taking an absolute worst case of 1\% either way.
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%
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$$ 5V.\frac{2k2*0.99}{2k2*1.01+2k2*0.99} = 2.475V $$
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%
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$$ 5V.\frac{2k2*1.01}{2k2*1.01+2k2*0.99} = 2.525V $$
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%
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These readings both lie outside the proscribed range.
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Also the sense+ and sense- readings would have the same value.
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%
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\paragraph{ TC 6 : Voltages $R_3$ OPEN }
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%
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Here the potential divider is broken. The sense- will read 0V and the sense+ will
|
||||
read 5V. Both readings are outside the proscribed range.
|
||||
|
||||
%
|
||||
\subsection{Summary of Analysis}
|
||||
|
||||
%
|
||||
All six test cases have been analysed and the results agree with the FMEA
|
||||
presented in table~\ref{ptfmea}.
|
||||
%The PLD diagram, can now be used to collect the symptoms.
|
||||
@ -2331,7 +2312,7 @@ In practical use, by defining an acceptable measurement/temperature range,
|
||||
and ensuring the
|
||||
values are always within these bounds, we can be confident that none of the
|
||||
resistors in this circuit has failed.
|
||||
|
||||
%
|
||||
\ifthenelse{\boolean{pld}}
|
||||
{
|
||||
\begin{figure}[h]
|
||||
@ -2342,8 +2323,8 @@ resistors in this circuit has failed.
|
||||
\label{fig:Pt100_tc_sp}
|
||||
\end{figure}
|
||||
}
|
||||
|
||||
|
||||
%
|
||||
%
|
||||
\subsection{Derived Component with one failure mode.}
|
||||
The Pt100 circuit can now be treated as a component in its own right, and has one failure mode,
|
||||
{\textbf OUT\_OF\_RANGE}. This is a single, detectable failure mode. The detectability of a
|
||||
@ -2353,7 +2334,7 @@ has been developed for safety critical temperature measurement.
|
||||
\ifthenelse{\boolean{pld}}
|
||||
{
|
||||
It can now be represented as a PLD see figure \ref{fig:Pt100_singlef}.
|
||||
|
||||
%
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=100pt,bb=0 0 167 194,keepaspectratio=true]{./CH5_Examples/Pt100_singlef.png}
|
||||
@ -2362,22 +2343,22 @@ It can now be represented as a PLD see figure \ref{fig:Pt100_singlef}.
|
||||
\label{fig:Pt100_singlef}
|
||||
\end{figure}
|
||||
}
|
||||
|
||||
%
|
||||
%From the single faults (cardinality constrained powerset of 1) analysis, we can now create
|
||||
%a new derived component, the {\emPt100circuit}. This has only \{ OUT\_OF\_RANGE \}
|
||||
%as its single failure mode.
|
||||
|
||||
|
||||
%
|
||||
%
|
||||
%Interestingly we can calculate the failure statistics for this circuit now.
|
||||
%Mill 1991 gives resistor stats of ${10}^{11}$ times 6 (can we get special stats for Pt100) ???
|
||||
%\clearpage
|
||||
|
||||
|
||||
|
||||
%
|
||||
%
|
||||
%
|
||||
%\section{Double failure analysis}
|
||||
|
||||
%
|
||||
%CITE PRICE MULTIPLE FAILURE PAPER.
|
||||
|
||||
%
|
||||
%\clearpage
|
||||
\section{ Pt100 Double Simultaneous Fault Analysis}
|
||||
\label{sec:Pt100d}
|
||||
@ -2398,7 +2379,7 @@ Table \ref{tab:ptfmea2} lists all the combinations of double
|
||||
faults as FMMD test cases.
|
||||
%and then hypothesises how the functional~group will react
|
||||
%under those conditions.
|
||||
|
||||
%
|
||||
\begin{table}[ht]
|
||||
\caption{Pt100 FMEA Double Faults} % title of Table
|
||||
\centering % used for centering table
|
||||
@ -2431,10 +2412,10 @@ TC 18: & $R_2$ SHORT $R_3$ SHORT & low & low & Both out of Rang
|
||||
\end{tabular}
|
||||
\label{tab:ptfmea2}
|
||||
\end{table}
|
||||
|
||||
|
||||
%
|
||||
%
|
||||
%\paragraph{Proof of Double Faults Hypothesis}
|
||||
|
||||
%
|
||||
\paragraph{ TC 7 : Voltages $R_1$ OPEN $R_2$ OPEN }
|
||||
\label{Pt100:bothfloating}
|
||||
This double fault mode produces an interesting symptom.
|
||||
@ -2451,84 +2432,84 @@ fault.
|
||||
%
|
||||
Undetectable faults are generally to be avoided in a safety critical environment~\cite{ACS:ACS1297,721666}.
|
||||
%that must be handled.
|
||||
|
||||
|
||||
%
|
||||
%
|
||||
\paragraph{ TC 8 : Voltages $R_1$ OPEN $R_2$ SHORT }
|
||||
|
||||
%
|
||||
This cuts the supply from Vcc. Both sense lines will be at zero.
|
||||
Thus both values will be out of range.
|
||||
|
||||
|
||||
%
|
||||
%
|
||||
\paragraph{ TC 9 : Voltages $R_1$ OPEN $R_3$ OPEN }
|
||||
|
||||
%
|
||||
Sense- will be floating.
|
||||
Sense+ will be tied to Vcc and will thus be out of range.
|
||||
|
||||
%
|
||||
\paragraph{ TC 10 : Voltages $R_1$ OPEN $R_3$ SHORT }
|
||||
|
||||
%
|
||||
This shorts ground to
|
||||
both of the sense lines.
|
||||
Both values will be out of range.
|
||||
|
||||
%
|
||||
\paragraph{ TC 11 : Voltages $R_1$ SHORT $R_2$ OPEN }
|
||||
|
||||
%
|
||||
This shorts both sense lines to Vcc.
|
||||
Both values will be out of range.
|
||||
|
||||
|
||||
%
|
||||
%
|
||||
\paragraph{ TC 12 : Voltages $R_1$ SHORT $R_2$ SHORT }
|
||||
|
||||
%
|
||||
This shorts the sense+ to Vcc and the sense- to ground.
|
||||
Both values will be out of range.
|
||||
|
||||
|
||||
%
|
||||
%
|
||||
\paragraph{ TC 13 : Voltages $R_1$ SHORT $R_3$ OPEN }
|
||||
|
||||
%
|
||||
This shorts the sense+ to Vcc and the sense- to ground.
|
||||
Both values will be out of range.
|
||||
|
||||
%
|
||||
\paragraph{ TC 14 : Voltages $R_1$ SHORT $R_3$ SHORT }
|
||||
|
||||
%
|
||||
This shorts the sense+ and sense- to Vcc.
|
||||
Both values will be out of range.
|
||||
|
||||
%
|
||||
\paragraph{ TC 15 : Voltages $R_2$ OPEN $R_3$ OPEN }
|
||||
|
||||
%
|
||||
This shorts the sense+ to Vcc and causes sense- to float.
|
||||
The sense+ value will be out of range.
|
||||
|
||||
|
||||
%
|
||||
%
|
||||
\paragraph{ TC 16 : Voltages $R_2$ OPEN $R_3$ SHORT }
|
||||
|
||||
%
|
||||
This shorts the sense+ and sense- to Vcc.
|
||||
Both values will be out of range.
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
%
|
||||
%
|
||||
%
|
||||
%
|
||||
%
|
||||
\paragraph{ TC 17 : Voltages $R_2$ SHORT $R_3$ OPEN }
|
||||
|
||||
%
|
||||
This shorts the sense- to ground.
|
||||
The sense- value will be out of range.
|
||||
|
||||
|
||||
%
|
||||
%
|
||||
\paragraph{ TC 18 : Voltages $R_2$ SHORT $R_3$ SHORT }
|
||||
|
||||
%
|
||||
This shorts the sense+ and sense- to Vcc.
|
||||
Both values will be out of range.
|
||||
|
||||
%
|
||||
%\clearpage
|
||||
|
||||
%
|
||||
\ifthenelse{\boolean{pld}}
|
||||
{
|
||||
\subsection{Double Faults Represented on a PLD Diagram}
|
||||
|
||||
%
|
||||
We can show the test cases on a diagram with the double faults residing on regions
|
||||
corresponding to overlapping contours see figure \ref{fig:plddouble}.
|
||||
Thus $TC\_18$ will be enclosed by the $R2\_SHORT$ contour and the $R3\_SHORT$ contour.
|
||||
|
||||
|
||||
%
|
||||
%
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=450pt,bb=0 0 730 641,keepaspectratio=true]{./CH5_Examples/plddouble.png}
|
||||
@ -2536,7 +2517,7 @@ Thus $TC\_18$ will be enclosed by the $R2\_SHORT$ contour and the $R3\_SHORT$ co
|
||||
\caption{Pt100 Double Simultaneous Faults}
|
||||
\label{fig:plddouble}
|
||||
\end{figure}
|
||||
|
||||
%
|
||||
We use equation \ref{eqn:correctedccps2} to verify complete coverage for
|
||||
a given cardinality constraint is not visually obvious.
|
||||
%
|
||||
@ -2546,22 +2527,22 @@ not that all for a given cardinality constraint have been included.
|
||||
}
|
||||
{
|
||||
}
|
||||
|
||||
%
|
||||
\paragraph{Symptom Extraction}
|
||||
|
||||
%
|
||||
We can now examine the results of the test case analysis and apply symptom abstraction.
|
||||
In all the test case results we have at least one out of range value, except for
|
||||
$TC\_7$
|
||||
which has two unknown values/floating readings. We can collect all the faults, except $TC\_7$,
|
||||
into the symptom $OUT\_OF\_RANGE$.
|
||||
As a symptom $TC\_7$ could be described as $FLOATING$.
|
||||
|
||||
%
|
||||
\ifthenelse{\boolean{pld}}
|
||||
{
|
||||
We can thus draw a PLD diagram representing the
|
||||
failure modes of this functional~group, the Pt100 circuit from the perspective of double simultaneous failures,
|
||||
in figure \ref{fig:Pt100_doublef}.
|
||||
|
||||
%
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=450pt,bb=0 0 730 641,keepaspectratio=true]{./CH5_Examples/plddoublesymptom.png}
|
||||
@ -2572,12 +2553,13 @@ in figure \ref{fig:Pt100_doublef}.
|
||||
} %% \ifthenelse {\boolean{pld}}
|
||||
{
|
||||
}
|
||||
|
||||
%
|
||||
%\clearpage
|
||||
\subsection{Derived Component : The Pt100 Circuit}
|
||||
\label{sec:Pt100floating}
|
||||
The Pt100 circuit again, can now be treated as a component in its own right, and has two failure modes,
|
||||
{\textbf{OUT\_OF\_RANGE}} and {\textbf{FLOATING}}.
|
||||
|
||||
%
|
||||
\ifthenelse{\boolean{pld}}
|
||||
{
|
||||
It can now be represented as a PLD see figure \ref{fig:Pt100_doublef}.
|
||||
@ -2591,9 +2573,9 @@ It can now be represented as a PLD see figure \ref{fig:Pt100_doublef}.
|
||||
} % \ifthenelse {\boolean{pld}}
|
||||
{
|
||||
}
|
||||
|
||||
|
||||
|
||||
%
|
||||
%
|
||||
%
|
||||
% The resistors R1, R2 form a summing junction
|
||||
% to the negative input of IC1.
|
||||
% Using the earlier definition for resistor failure modes,
|
||||
@ -2621,18 +2603,17 @@ It can now be represented as a PLD see figure \ref{fig:Pt100_doublef}.
|
||||
%
|
||||
% This summing junction fails with two symptoms. We create a {\dc} called $SUMJUNCT$ and we can state,
|
||||
% $$fm(SUMJUNCT) = \{ R1\_IN\_DOM, R2\_IN\_DOM \} $$.
|
||||
|
||||
|
||||
%
|
||||
%
|
||||
%The D type flip flop
|
||||
|
||||
%
|
||||
%\subsection{FMMD Process applied to $\Sigma \Delta $ADC}.
|
||||
|
||||
%
|
||||
%T%he block diagram in figure~\ref{fig
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
|
||||
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
@ -19,11 +19,11 @@ the University of Brighton, pushing me forward in clarity of self-expression,
|
||||
precision through mathematics, critical assessment and carefully crafted English:
|
||||
its members will always remain dear to me.
|
||||
%
|
||||
%%%% IS THIS BIT A BIT MAD????
|
||||
Like an army recruits training Sergeant Major I found them
|
||||
hard task masters at first, and then, as with realising the rationale behind training and
|
||||
{\em even} parade drill, respected and grew to like them.
|
||||
%
|
||||
%%%% IS THIS BIT A BIT MAD???? YES! 27AUG2013
|
||||
% % % Like an army recruits training Sergeant Major I found them
|
||||
% % % hard task masters at first, and then, as with realising the rationale behind training and
|
||||
% % % {\em even} parade drill, respected and grew to like them.
|
||||
% % % %
|
||||
%
|
||||
My first debt of gratitude must go to my supervisors,
|
||||
Dr. A. Fish,
|
||||
|
||||
@ -9,6 +9,7 @@
|
||||
|
||||
|
||||
\newcommand{\ft}{\ensuremath{4\!\!\rightarrow\!\!20mA} }
|
||||
\newcommand{\tenfifty}{\ensuremath{10\!\!\rightarrow\!\!50mA} }
|
||||
\usepackage{graphicx}
|
||||
\usepackage{fancyhdr}
|
||||
\usepackage{tikz}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user